Definition:Dynamical System/Flow

Definition

In a dynamical system, a set of time-dependent equations is known as flow.

This article is complete as far as it goes, but it could do with expansion. In particular: Nelson has this as "The term [ dynamical system] is also used to describe a point or set of points whose positions evolve with time according to a set of time-dependent equations or flow, typically the solution to a set of differential equations." You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding this information. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Expand}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Examples

Arbitrary Example

Let the position of a point $x$ at time $t$ be denoted $\map x t$.

The equation $\map x t = t^2 + 1$ defines a flow on the real number line which is a solution to the differential equation $\map {x'} t = 2 t$.

Also see

• Results about dynamical systems can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): dynamical system
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): flow
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): dynamical system
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): flow